## Related questions with answers

An electronic package with a surface area of $1 m^2$ placed in an orbiting space station is exposed to space. The electronics in this package dissipate all 1 kW of its power to the space through its exposed surface. The exposed surface has an emissivity of 1.0 and an absorptivity of 0.25. Determine the steady state exposed surface temperature of the electronic package (a) if the surface is exposed to a solar flux of $750 W/m^2,$ and (b) if the surface is not exposed to the sun.

Solution

Verified$\text{\textcolor{#c34632}{\textbf{(a)}}}$

```
The steady state temperature in this case is determined by equating the generated heat rate by the emitted heat rate as following,
```

$\begin{align*} \dot{Q}_\text{gen}&=\dot{Q}_\text{emit}\\ \dot{Q}_\text{gen}&=\varepsilon \sigma A T_s^4\\ 1000&=1*5.67*10^{-8}*1*T_s^4 \end{align*}$

```
Hence, the package surface area in this case is
```

$\color{#c34632}{T_s=364.42\ \text{K}}$

```
$\text{\textcolor{#c34632}{\textbf{(b)}}}$
The steady state temperature in this case is determined by equating the generated heat rate and the absorbed heat rate by the emitted heat rate as following,
```

$\begin{align*} \dot{Q}_\text{gen}+\dot{Q}_\text{abs}&=\dot{Q}_\text{emit}\\ \dot{Q}_\text{gen}+\alpha A\dot{q}_\text{sol}&=\varepsilon \sigma A\\ T_s^4 1000+0.25*1*750&=1*5.67*10^{-8}*1*T_s^4 \end{align*}$

```
Hence, the package surface area in this case is
```

$\color{#c34632}{T_s=380.42\ \text{K}}$

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